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Results (16 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=c^{16}=[a,b]=1, b^{2}=c^{8}, c^{a}=c^{9}, c^{b}=c^{7} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $Q_{32}:C_2$ | 1A | $1$ | $1$ | $Q_{32}:C_2$ | 1A | $1$ |
| $Q_{32}:C_2$ | 2A | $2$ | $1$ | $Q_{32}:C_2$ | 1A | $c^{8}$ |
| $Q_{32}:C_2$ | 2B | $2$ | $2$ | $C_2\times Q_{16}$ | 1A | $a$ |
| $Q_{32}:C_2$ | 2C | $2$ | $8$ | $C_2\times C_4$ | 1A | $bc$ |
| $Q_{32}:C_2$ | 4A | $4$ | $2$ | $D_8:C_2$ | 2A | $ac^{4}$ |
| $Q_{32}:C_2$ | 4B | $4$ | $2$ | $\OD_{32}$ | 2A | $c^{4}$ |
| $Q_{32}:C_2$ | 4C | $4$ | $8$ | $C_2\times C_4$ | 2A | $b$ |
| $Q_{32}:C_2$ | 4D | $4$ | $8$ | $C_2\times C_4$ | 2A | $ab$ |
| $Q_{32}:C_2$ | 4E | $4$ | $8$ | $C_2\times C_4$ | 2A | $abc$ |
| $Q_{32}:C_2$ | 8A1 | $8$ | $2$ | $\OD_{32}$ | 4B | $c^{2}$ |
| $Q_{32}:C_2$ | 8A3 | $8$ | $2$ | $\OD_{32}$ | 4B | $c^{6}$ |
| $Q_{32}:C_2$ | 8B | $8$ | $4$ | $C_2\times C_8$ | 4B | $ac^{2}$ |
| $Q_{32}:C_2$ | 16A1 | $16$ | $4$ | $C_{16}$ | 8A1 | $c$ |
| $Q_{32}:C_2$ | 16A3 | $16$ | $4$ | $C_{16}$ | 8A3 | $c^{5}$ |
| $Q_{32}:C_2$ | 16B1 | $16$ | $4$ | $C_{16}$ | 8A3 | $ac$ |
| $Q_{32}:C_2$ | 16B3 | $16$ | $4$ | $C_{16}$ | 8A1 | $ac^{5}$ |